The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of the function near a particular value of its independent variable. The limit of a function at is if for every , there exists a such that implies . That is, if is within any arbitrary distance of whenever is sufficiently close, but not necessarily equal to, . Note that represents the greatest distance between the values of the function and its limit, while represents the distance from the values of the function's inputs to . If, by chance, we have , then we also say that is continuous at .
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| - The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of the function near a particular value of its independent variable. The limit of a function at is if for every , there exists a such that implies . That is, if is within any arbitrary distance of whenever is sufficiently close, but not necessarily equal to, . Note that represents the greatest distance between the values of the function and its limit, while represents the distance from the values of the function's inputs to . If, by chance, we have , then we also say that is continuous at .
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abstract
| - The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of the function near a particular value of its independent variable. The limit of a function at is if for every , there exists a such that implies . That is, if is within any arbitrary distance of whenever is sufficiently close, but not necessarily equal to, . Note that represents the greatest distance between the values of the function and its limit, while represents the distance from the values of the function's inputs to . The idea that the condition is not required allows for the possibility that the values of function approaches , but the actual value of need not be , or even defined. If, by chance, we have , then we also say that is continuous at .
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